Acceleration Due to Gravity

The force of gravity pulls down on all objects on earth. If the objects are allowed to fall they accelerate downwards.

If there is no air resistance or friction then all objects accelerate downwards at the same rate. You may have heard of a famous experiment that Galileo is supposed to have done from the leaning tower of Pisa: if a heavy stone and a light stone are dropped together, they accelerate at the same rate and land at the same time.

Accurate measurements show that the acceleration due to gravity = 9.8m/s�.

For simple calculations we usually 10 m/s�.

This means that for an object falling with no air resistance, the velocity after 1 second is 10 m/s, and after 2 seconds the velocity is 20 m/s, and so on.

In practise there is usually air resistance. If a person free falling falls along without a parachute, then because of friction they will reach a final or terminal velocity of about 50 m/s – the speed of a fast racing car.

A parachute is designed to make the air resistance as large as possible. With a parachute terminal velocity is only 8 m/s.

At terminal velocity, the forces on an object are balanced:

Force of gravity (weight) = Force of air resistance

(Downwards) (Upwards)

This is an example of Newton’s First Law: because there is no resultant force on the object it continues to move at constant speed in a straight line.

Aim:-

In this experiment I am planning to investigate if the effects of the wing size of the spinner determine the speed at which the spinner falls and therefore the length of time it takes to reach the floor when dropped from a height of 1 metre.

Apparatus:-

; 3 x Paper spinner

; paper clips

; 2 x 1 metre ruler

; clamp stand

; scissors

; pencil

Prediction:-

I predict that the shorter the wings of the spinner the shorter time it will take for it too reach the floor and the faster it will fall. I think this will happen because the surface area of the wings will be smaller

Preliminary Work: –

; How to make the spinner

Here is the outline of the spinner:-

To produce the spinner u cut along all the solid lines and fold along all the dotted lines. The fold part a forwards and Part B backwards this produces the wings of the spinner. To produce the body u fold in part D and then part C so part C overlaps part D. This part is then held together with a paper clip.

; Basic Physics behind the paper Spinner

As the spinner falls through the air, it spins. The basic explanation for this is related to the position of the wings during its flight. As the spinner falls downward, two forces act on it: its weight and the resistive force. The resistive force is provided in the form of air resistance, almost entirely by the wings.

The wings will pulled upwards as almost all of the air resistance is acting on them as paper is normally a very flexible substance the wings bend up. So, in flight, the wings will take a curved shape, with the parts of the wings further from the body bending up more.

When falling, the air will be flowing past the wings, and will be deflected by them. Because the wings are deflecting the air, they are therefore exerting a force on the air. Newton’s third law states that every force has an equal and opposite force acting as a reaction in the opposite direction. From this we can deduce that the air exerts a force on the wings:

There will obviously be a horizontal component to the forces on the wings. Looking at these horizontal forces from the point of view of the above the diagram, they will be acting towards the body of the spinner. Below is a diagram showing the horizontal components of these forces acting on the wings, from above the spinner.

Because there are forces acting on different sides of the spinner, and in opposite directions, the spinner will spin (anti-clockwise in this diagram).

Preliminary Results: –

Length of Spinner Wings (cm)

Area of Spinner wings (cm�)

Time the spinner takes to fall 1 metre (secs)

7

10.5

1.08

6

9

0.93

5

7.5

0.83

4

6

0.67

3

4.5

0.44

2

3

0.29

1

1.5

0.17

Diagram: –

Method: –

To take my readings I will drop my spinner from a height of 2 metres and measure the time taken for the spinner to fall from when it reaches the top of the 1 metre rule to the floor. Firstly I will set up the experiment as shown in the diagram above. I will use both arms of the clamp stand 1 for each ruler. I will make and cut out the spinner I will start with the wing length of 7 cm and each time I will repeat the experiment 3 times. Once I have recorded my results for the 7 cm wings I will then cut a centimetre off each wing each time so that I will finally end up with a spinner with wing length of just 1 cm. I am going to drop the spinner from the top of the first ruler. As I am not tall enough to reach I will stand on the desk but will be careful as explained in the safety. I will then start the stop clock when the spinner reaches the top of the second ruler, by this time the spinner will have reached terminal velocity, and will stop it when it reaches the ground. I will record my results in the table below. From each of my results I will work out the average for each of the lengths and will also record this. I will produce of graph of these results. Then to gain a better conclusion I will work out the velocity for each of the averages for each wing length using the equation

Velocity = distance travelled

Time taken

V = D

t

With this data I can plot a velocity time graph.

Safety: –

My experiment isn’t really dangerous but I will have to be careful when using scissors to cut out the spinner as I don’t cut my hand or finger and I will also have to be careful when standing on the table to drop the spinner as I don’t fall off so to reduce the risk of a serious injury I am going to place stools all around the table so if I accidentally step off the table the distance will be much smaller to the stool than too the floor

Results: –

Length of Spinner Wings (cm)

Area of Spinner wings (cm�)

Time the spinner takes to fall 1 metre (secs)

1st time

2nd time

3rd time

Average

7

10.5

1.22

1.24

1.14

1.20

6

9

0.87

0.87

0.86

0.87

5

7.5

0.63

0.68

0.71

0.67

4

6

0.52

0.54

0.51

0.52

3

4.5

0.39

0.42

0.45

0.42

2

3

0.30

0.29

0.27

0.29

1

1.5

0.19

0.23

0.22

0.21

Length of Spinner Wings (cm)

Area of Spinner wings (cm�)

Average Time spinner takes to fall 1 metre

Average Speed at which the spinner falls (m/s)

7

10.5

1.20

0.83

6

9

0.87

1.15

5

7.5

0.67

1.49

4

6

0.52

1.92

3

4.5

0.42

2.38

2

3

0.29

3.45

1

1.5

0.21

4.76

Conclusion: –

From my results I know that the object I was testing experienced air resistance because otherwise, if the objects were falling through an empty space, they would fall with a constant acceleration of 10m/s2 due to gravity. Falling objects also experience an upward force due to friction between the object and the air. The faster the object moves, the greater the force of friction. The greater the air resistance, the more resistance there is against movement; therefore it takes less time until air resistance (drag) becomes the same as the downwards force (gravity). The faster the spinner were falling, the more air resistance was created therefore slowing down the acceleration. The object is accelerating for a, longer time resulting in a reduced terminal velocity. The length of wings of the spinners I was testing obviously affected the overall speed and acceleration.

Analysis: –

From my graphs that I have drawn I can see that there is a relationship between the length of the wings of the spinner and the time taken for it to fall 1 metre. From the graph of the length of the spinners wings against time I conclude that as the length of the wings increase the time taken to fall 1 metre increases this is because the spinner has a greater area and therefore greater air resistance so the speed of fall is slower and therefore the time longer.

Most of my results on the graph of length of spinner’s wings against time appear to fall on a curved line. None of them seem to fall out of the curve of the line. I predicted that the time would be longer when the spinner had larger wings with greater surface area and I would have thought that by doubling the area of the spinner I would be doubling the air resistance and therefore doubling the time. This is not what I found since my graph is a curve line and not a straight line of best fit.

The graph of length of wings against velocity shows that as the length of the wings increases the average velocity of the fall decreases foe example when the length is 2 cm the average velocity is 3.4m/s and at 4 cm it is 1.9m/s. The graph is a curve which means that a 1 cm difference in length of wing makes a bigger difference to the change in speed from 1 to 2 cms than from 6 to 7 cms.

The graph of area of wing against time shows that as the area increases the time increases. This is due to the increased air resistance caused by an increase in the number of particles colliding with the wings of the spinner as it falls. The bigger wing causes a bigger upward force which offsets the weight downwards to a greater extent causing the downward resultant force to be less and therefore the acceleration less and therefore the time greater.

The velocity time graph shows that as time increases velocity decreases. The acceleration of any object is the change in speed divided by time. We do not have the final speed only the average speed but since the greater the final velocity the greater the average speed then we can use the steepness of the graph to give some indication of the acceleration of the different sizes of wings. At smaller times which mean smaller wing sizes the graph is very steep giving a larger acceleration whereas at larger times from the greater wing size the graph is shallow and therefore the gradient smaller. This suggests a much smaller acceleration.

Evaluation: –

Although I think the results of my experiment where reliable as I repeated and took averages. I feel that the 1cm results aren’t quite as reliable as the rest. I feel this because the results where very close to my reaction time. Also it was hard to see when the spinner reached terminal velocity even though it spins each time. However I still used the results of the 1cm spinner as this allowed me to draw a better line of best fit. This is because without this result the line of best fit looked as though it was a straight line that passed straight through the origin however this could not be the case as it would still take time as even a spinner with no wings would take time to reach the floor. Although it would be quick it would still take longer than 0.00secs.

If I was to repeat the experiment again I would change the way I carried out the experiment in certain areas to give me more valid and accurate results. For instance I could perhaps use more accurate ways of measuring the time for example instead of just using a stop clock and my trusty eye I could use a photo detector, this is when a timer starts due to a light beam being broken and this case that would be by the spinner and it would be stopped by a very sensitive switch pad on the floor when the spinner hits it. This would make my results more reliable as the stop clock would be started at exact times and it would rule out my reaction time.

When I constructed my line of best fit I thought that the points lay on a curve however I have no guarantee of this fact. In order to confirm the shape of the graph I could have taken some values between the points completed. For example I could have used a length of 1.1, 1.2, 1.3, 1.4, etc. This would have been to time consuming and the differences in the times so small that my results would have been difficult to plot. However the scattered points produced by these extra experiment could have gone a long way to confirming the curved shape of the graph.

Although I thought the first point was an anomalous point due to the fact that I made an assumption that it was a straight line graph, once I had established that it was a curve most of the points seem to fall on or close to the curve. The three centimetre length of wing seems to have a time that is a little long and if I had time I would have liked to have repeated this result again.

To extend my investigation in the future I could see if other distances other than 1 metre would give the same results if I chose a much greater distance than 1 metre I could ensure that terminal velocity had been reached. Also a greater distance than 1 metre would mean longer times and therefore my reaction would have a less significant effect.

I could also investigate what other variables affect the spinner for example it would be interesting to see what effect weight would have on the time the spinner takes to fall 1 metre if any effect at all. This would show if there was a relationship between weight and time taken.